Does Gibrat's Law hold among young,small firms?

According to Gibrat's Law of Proportionate Effect, the growth rate of a given firm is independent of its size at the beginning of the examined period. Aimed at extending this line of investigation, the present paper uses quantile regression techniques to test whether Gibrat's Law holds for new entrants in a given industry: that is for new small firms in the early stage of their life cycle. The main finding is that for some selected industries in Italian manufacturing Gibrat's Law fails to hold in the years immediately following start-up, when smaller firms have to rush in order to achieve a size large enough to enhance their likelihood of survival. Conversely, in subsequent years the patterns of growth of new smaller firms do not differ significantly from those of larger entrants, and the Law therefore cannot be rejected.JEL Classification: L11, L60Previous versions of this paper were presented at the 27th Annual EARIE Conference (Lausanne, 7-10 September 2000) and at seminars held between 2000 and 2003 at the Economics Department of Harvard University, the Catholic University of Milan, the University of Ferrara, the University of Bologna, the Bank of Italy, and Athens University of Economics & Business. We would like to thank Carlo Bianchi, Giuseppe Colangelo, Giovanni Dosi, Steven Klepper (Editor), Stephen Martin, Ariel Pakes, Aman Ullah and, in particular, Helen Louri and two anonymous referees for their valuable comments on earlier drafts. Financial support from MIUR (Year 2000; protocol #MM13038538_001; project leader: E. Santarelli) is gratefully acknowledged.Correspondence to: E. Santarelly     

Cournot and Stackelberg Duopolies Revisited

First, conditions are derived for a leader (or a follower) to be more advantageous than a follower (or a leader) in Stackelberg duopoly with symmetric firms and without product differentiation. Second, the equilibria in Cournot and Stackelberg duopolies are compared under a set of reasonable assumptions. If the reaction function slopes upward, the Cournot duopolists' profits turn out to be lower than those of both the Stackelberg leader and follower, and the equilibrium industry output is smaller in Stackelberg duopoly than in Cournot duopoly.
JEL Classification Numbers: D21, D43, L13.     

Second Mover Disadvantages in a Three-Player Stackelberg Game with Private Information

I consider a three-player Stackelberg. game where each player has its private signal concerning stochastic demand. I show that at a perfectly revealing equilibrium, the second mover earns the lowest and the third mover the highest expected profit of the three. I characterize this result by the strategic substitutes or complements relationships among three firms at the equilibrium. Journal of Economic Literature Classification Numbers: C72, D82, and L13.     

To Commit or Not to Commit: Endogenous Timing in Experimental Duopoly Markets

In this paper we experimentally investigate the extended game with action commitment of Hamilton and Slutsky (1990, Games Econ. Behavior2, 29–46). In their duopoly game firms can choose their quantities in one of two periods before the market clears. If a firm commits to a quantity in period 1, it does not know whether the other firm also commits early. By waiting until period 2, a firm can observe the other firm's period-1 action. Hamilton and Slutsky predicted the emergence of endogenous Stackelberg leadership. Our data, however, do not confirm the theory. While Stackelberg equilibria are extremely rare, we often observe endogenous Cournot outcomes and sometimes collusive play. This is partly driven by the fact that endogenous Stackelberg followers learn to behave in a reciprocal fashion over time, i.e., they learn to reward cooperation and to punish exploitation. Journal of Economic Literature Classification Numbers: C72, C92, D43.     

Endogenous Timing with Incomplete Information and with Observable Delay

This paper analyzes endogenous timing in a duopoly model with incomplete information. Firms announce the period in which they will move before choosing an action and are then committed to their choices. Endogenous Stackelberg equilibria, with either the informed or the uninformed firm as the Stackelberg leader, may emerge. For most parameters, the Cournot equilibrium in the first production period results endogenously. Journal of Economic Literature Classification Numbers: C72; C73; D82; L10.     

Exploring larger biotech research firm strategies: Projections from a comparison of small and larger firms

This is an exploratory study of larger biotech firms using insights from a head-to-head comparison of 49 small and 17 large U.S. biotech firms using archival data. We found small and large biotech firms to be significantly different from each other on R&D intensity and funding strategies. The findings are used to project and hypothesize about larger biotech firm growth strategies.Whereas R&D expenses in the small firms exceed total income by a wide margin, larger firms are able to cover most, if not all, of their R&D expenses. Thus, the larger firms are relatively more financially viable. Results also show that the larger firms derive a greater proportion of their revenues from collaborative research agreements (CRAs), which has key implications for revenue growth in these firms.Based on the findings we project R&D expenses and collaborative research revenues for biotech firms as they grow in size.     

Commitment,first-mover-, and second-mover advantage

We identify circumstances under which a firm with a first-mover advantage may get leapfrogged by a follower. At the market stage we assume a Stackelberg structure, i.e. the leader commits to a quantity and the follower reacts to it. We allow the owners of both firms to select the internal organization and the production technology before quantities are set. That is, leader and follower can additionally use two commitment strategies alternatively or in combination: investing in R&D and delegating quantity decisions to managers. Despite the symmetry of options for the two firms, we find that there is a unique equilibrium in which both firms invest in process R&D, only the follower delegates, and the follower can overcome the first-mover advantage of the quantity leader and obtain a higher profit than the leader. Our analysis reveals that there are some important differences between the two commitment devices “cost-reducing R&Dt” and “delegation to managers”.      

Cost Reduction,Licensing and Incentive to Innovate: A Note

In this Note we consider an economy composed by two firms; a leader and a follower, that invest in R&D for process innovations. Competition to innovate is usually modelled as a two stage game. In the first stage of the game both firms simultaneously reduces their production costs. In the second stage the firms compete la Stackelberg and it is possible to prove that the profits of one of the two firms (and total profits) might decrease in a range of parameters. Then we consider the possibility of technology transfer from the leader that has the most productive technology to the follower under licensing by means of a fixed fee and of a royalty. It is possible to prove that under licensing total profits will increase in some range of parameters above mentioned in comparison to the pre-innovation case.     

Non-renewable resource Stackelberg games

The market structure for many mineral industries can be described as oligopoly with potential for Stackelberg leadership. This paper derives and analyzes dynamically consistent extraction equilibria in a two-period discrete-time “Truly” Stackelberg (TS) model of non-renewable resource extraction, where firms move sequentially within each period and where both the leader and follower have market power. We show how the leader may be able to manipulate extraction patterns by exploiting resource constraints. Whether the leader wants to speed up its own production relative to the Cournot–Nash (CN) equilibrium depends on the shape of its iso-profit curve, which is affected by the two firms’ relative stock endowments and relative production costs. If the leader extracts faster, then the follower extracts slower, but in aggregate the industry extracts faster. Unlike static Stackelberg games, the follower does not necessarily have a second mover disadvantage.     

The stability of generalised stackelberg equilibria in heterogeneous oligopoly

Conclusions In this paper we have derived sufficient conditions for the stability of the G. S. E. These conditions follow from the condition on the stability of the G. C. E., given by Okuguchi (1978).When the conditions for asymptotic stability are fulfilled, the existence of the G. S. E. may be demonstrated in the same way as the existence of the G. C. E. has been demonstrated by Okuguchi (1978), that is: the G. S. E. is the fixpoint of a contracting mapping. In the case of linear demand functions and quadratic cost functions we have found the rather strong result that the sufficient conditions for (asymptotic) stability of the G. C. E. imply the (asymptotic) stability of the G. S. E. as well.This conclusion may be surprising to followers of Stackelberg. Mostly the outcome of a Stackelberg oligopoly is considered as adisequilibrium.In this paper we have made clear that a firm maximizing expected profit and using a generalised Stackelberg strategy, like a firm using a generalised Cournot strategy, only correctly predicts inequilibrium the price of the other firms. (See also on this point Heertje and Furth (1979)).When the outcome of a G. S. E. gives one or more firms less profit than in a G. C. E. then they expect, any price change, under-taken by them, will lower their expected profit even more.I would like to thank Prof. Dr. A. Heertje and an anonymous referee for their useful comments on earlier drafts of this paper and D. Weatherall for his remarks on the english of the text.     

Duopoly Competition with Corporate Social Responsibility

This paper highlights the effect of firms’ position on firms’ strategies with corporate social responsibility (CSR) practices under three different cases: Cournot competition; Stackelberg competition with the CSR firm taking the leader position and turnover, with the profit maximising (PM) firm playing as the leader. Some interesting conclusions are achieved. First, the CSR firm always produces more than the PM firm. Second, the outputs of both firms (the consumer surplus) under the PM firm's leading position are larger than those under Cournot. Third, the profits of both firms (producer surplus) under the PM firm playing the leading position are less than those under Cournot. Surprisingly, when the PM firm first moves, the PM firm's profits are the lowest while the CSR firm's outputs are the highest in all three cases. Finally, the relationship of social welfare under the three cases is ambiguous.     

Firm Scale and the Endogenous Timing of Entry: a Choice between Commitment and Flexibility

This paper presents a model of stochastic oligopoly with demand uncertainty where firms endogenously choose entry timing. We examine two extreme types of market structure and show that the equilibrium correspondence that connects them is continous. With two identically sized firms, there are symmetric, Cournot type equilibria where the probability of early entry declines with greater uncertainty, and for low uncertainty two asymmetric equilibria. With one large firm with a continuum of nonatomic firms, there is a unique Stackelberg equilibrium. We conclude that the behavior of a dominant firm with a finite fringe can be approximated by Stackelberg equilibrium.Journal of Economic LiteratureClassification Numbers?: D21, L11.     

Stackelberg leadership with product differentiation and endogenous entry: some comparative static and limiting results

Allowing for endogenous entry in the traditional Stackelberg setup with product differentiation, leads to reverting of the standard comparative static and limiting results. Unlike in the standard Stackelberg setup with barriers to entry, the leader??s profit increases when the differentiation becomes lower. The reason is that competition becomes tougher when products become more alike, and consequently, fewer firms enter in equilibrium. On the other hand, increasing product differentiation towards its limit results in number of entrants tending to infinity and for very large market, the profit of the leader approaches zero. Thus market structure approaches monopolistic competition, rather than the standard monopoly outcome that occurs with exogenous number of followers.     

Corporate social responsibility and strategic relationships

We analyze a delegation game relevant to the conduct of corporate social responsibility (CSR) in which the firm’s owner offers the manager a contract consisting of firm profit and social welfare. We derive three results that distinctly differ from existing findings. First, CSR decisions are strategic complements for firms. Second, with simultaneous CSR decisions, the equilibrium price is equal to marginal cost, despite the fact that firms compete in a Cournot duopoly. Finally, with sequential CSR decisions, unlike the follower firm, the leader firm never exhibits CSR. However, the follower firm can enjoy a profit equal to that derived by the leader in a Cournot–Stackelberg game.     

Price leadership in a duopoly with capacity constraints and product differentiation

This paper analyzes Stackelberg price leadership in a duopoly in which firms are capacity constrained and products are imperfect substitutes. Assuming symmetric substitutes, linear demand, and efficient rationing, we characterize the equilibria with an exogenously specified leader. Using the equilibrium profits derived from these games, we argue that over certain ranges of asymmetric capacities an endogenous price leader will emerge. When endogenous leadership does arise, it is the large capacity firm which is the leader. We thus provide a game theoretic model of dominant firm price leadership.Dave Furth's research has been undertaken as a part of the project Competition and Cooperation. Dan Kovenock has benefited from financial support from Erasmus University Rotterdam, the Krannert School of Management, and the Jay N. Ross Young Faculty Research Fellowship. We are grateful to Tom Faith for valuable research assistance. We have benefited from the comments of the editor, two anonymous referees, and participants at the European meetings of the Econometric Society in September 1989 and the North American Winter Meetings of the Econometric Society in December 1989.     

A cake for Cournot

A cake division mechanism is presented that is equivalent in terms of the size of the pieces of the cake n players’ receive in equilibrium to the quantities that n firms in a Cournot oligopoly supply in equilibrium. This mechanism extends to equivalence between cake division and Nash’s ‘divide the dollar’ game.     

Playing Cournot although they shouldn’t

Summary. In this note, we experimentally investigate the extended game with action commitment in a Cournot duopoly with asymmetric cost. Risk dominance considerations allow to select a unique equilibrium in which the low-cost firm is the Stackelberg leader. The data, however, do not support the theory as simultaneous-move play is modal. Average output choices are in line with the Cournot equilibrium. This suggests that Cournot is a much more robust predictor for competition in markets than theory suggests.Received: 14 October 2002, Revised: 1 December 2003, JEL Classification Numbers: C72, C92, D43. Correspondence to: Hans-Theo Normann     

ALTERNATIVE STRATEGIES OF A PUBLIC ENTERPRISE IN OLIGOPOLY REVISITED: AN EXTENSION TO STACKELBERG COMPETITION

This paper revisits De Fraja and Delbono (1989), which is the seminal paper on mixed oligopoly, in order to pay more attention to Stackelberg competition. First, we show that, even in Cournot competition, if the number of private firms is sufficiently small, privatization necessarily reduces social welfare. Second, we demonstrate that when a public firm is a Stackelberg leader before and after privatization, privatization necessarily reduces welfare irrespective of the number of private firms. Moreover, we show that even when a public firm remains a follower, privatization reduces welfare if the number of private firms is relatively small.     

Negative externalities and Sen’s liberalism theorem

Summary. Sen’s seminal, negative theorem about minimal liberalism has had a profound effect on economics, philosophy, and the social sciences. To address concerns raised by his result, we show how Sen’s assumptions must be modified to obtain positive conclusions; e.g., one resolution allows an agent to be decisive only if his choice does not impose “strong negative externalities” on others. We also uncover a significantly different interpretation of Sen’s societal cycles: rather than describing the rights of individuals to choose, the cycles identify when these choices impose difficulties on others. Other ways to address Sen’s difficulties come from game theory.Received: 14 October 2004, Revised: 7 March 2005, JEL Classification Numbers: D71, C70, D62.Donald G. Saari: Correspondenc toThe research of D. Saari was supported by NSF grant DMI-0233798. Our thanks to P. Hammond for suggesting some useful references. Some of our joint results were reported in Brunel (now Petron) (1998).     

Consistency and optimality in a dynamic game of pollution control I: Competition

I model the interaction between a regulator and polluting firms as a Stackelberg differential game in which the regulator leads. The firms create pollution, which results in a stock extermality. I analyze the intertemporal effects of alternate pollution control measures in a competitive industry. The principal issue here concerns the dynamic inconsistency of the optimal solution. Inter alia, I compare the steady state levels of pollution under optimal and under time consistent policies.